Theorems · Definition · category theory

CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        [inst_2 : CategoryTheory.MonoidalCategory D] →
          [inst_3 : CategoryTheory.BraidedCategory D] →
            CategoryTheory.Functor.id (CategoryTheory.CommMon (CategoryTheory.Functor C D)) ≅
              CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor.comp
                CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse

The unit for the equivalence CommMon (C ⥤ D) ≌ C ⥤ CommMon D.

Defined in

Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory

Cited by

3 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory